F=ma, kinematics in vector notation

[shawli]

I'd like to go over my approach to a question I am doing right now, but I've posted my general approach instead of the question itself.

Say there is some object with three forces acting on it, and these forces are given to me in vector notation (i.e. with unit vectors "i" and "j"). I am also given the acceleration of the object as a scalar value with no direction/angle, only the unit "m/s²". If I am asked to find the velocity components of the object at time "t" (assuming initial t=0), is the following approach correct:

1. Add x-components and y-components of all three force vectors, which will give me the vector of the resultant/net force.
2. Find the angle "theta" of the net force using inverse tan.
3. Find velocity using Vf=Vi+a*t, where Vi=0 and "a" and "t" are given.

Here is where I am unsure:

4. Find x-component of velocity by Vf*cos(theta) and y-component of velocity by Vf*sin(theta). I am using the theta found in step 2, assuming the direction of the velocity is the same as the direction of the net force.

I'd like to know if my assumption about using the same theta is correct?

Thank you for reading this far!

 

[Ignea_unda]

I'd like to go over my approach to a question I am doing right now, but I've posted my general approach instead of the question itself.

Say there is some object with three forces acting on it, and these forces are given to me in vector notation (i.e. with unit vectors "i" and "j"). I am also given the acceleration of the object as a scalar value with no direction/angle, only the unit "m/s²". If I am asked to find the velocity components of the object at time "t" (assuming initial t=0), is the following approach correct:

1. Add x-components and y-components of all three force vectors, which will give me the vector of the resultant/net force.
2. Find the angle "theta" of the net force using inverse tan.
3. Find velocity using Vf=Vi+a*t, where Vi=0 and "a" and "t" are given.

Here is where I am unsure:

4. Find x-component of velocity by Vf*cos(theta) and y-component of velocity by Vf*sin(theta). I am using the theta found in step 2, assuming the direction of the velocity is the same as the direction of the net force.

I'd like to know if my assumption about using the same theta is correct?

Thank you for reading this far!

Assuming that either (a) the initial velocity, Vi, is zero, or (b) the initial velocity is at the same angle as the resultant force, you are correct.

 

[shawli]

Thank you for your speedy reply :D